Tetration, Zeration

For positive integers,
Multiplication is the same as repeated addition.
Exponentiation is the same as repeated multiplication.
There are two ways to go with this: what is repeated exponentiation? and what, repeated, is addition?
Repeated exponentiation is known as tetration.
The step below addition might be the increment operator (adding one.) Another possibility is called zeration. Both have some things going for them.

Any of these functions can be extended to work on real numbers. The picture is from the wikipedia article on tetration. I thought it was pretty.

Swiss automata

http://www.youtube.com/watch?v=uie8sqwQK7k



These are automata from Switzerland.

Good Books

Here's a list of some of my favorite books, books I've read at least twice. Some of the titles stand for the whole series. Most of these books I read ten or twenty years ago; I find I'm reading less fiction and more nonfiction these days. There's no ranking of the titles on this list, and I wasn't careful about exact titles.

Fantasy
Lord of the Rings
Watership Down
Alvin Maker
Dragonbone Chair
Chronicles of Amber (the first few)
Narnia
Wizard of Earthsea
Dragonriders of Pern (the original trilogy and the Dragonsinger trilogy)
The Crystal Cave (The first two books, the ones about Merlin)
The Last Unicorn
A Wrinkle in Time
The Dark is Rising
Fortress in the Eye of Time (this is one you may not have seen, by C.J. Cherryh)
Neverending Story
The Once and Future King
Oz (honestly, these Oz books don't hold up so well as an adult. The first and second books and the one with the Gnome King were the best of the lot. The illustrations are great.)

Science Fiction
Ender's Game
Dune (I could never really get into the sequels.)
Last and First Men (very early SF. I like it more for the ambition than the story.)
Foundation (the original trilogy)
Foreigner (I also liked the Pride of Chanur series.)
Snow Crash
The Diamond Age
Difference Engine (Maybe Stephenson is a little overrepresented on this list.)
Neuromancer (the whole series)
A Canticle for Leibowitz
Martian Chronicles
Tunnel in the Sky (My favorite Heinlein novel.)
Hyperion

Other
Pride and Prejudice
Moby Dick (Best read in small pieces. Treat it like a blog.)
Foucalt's Pendulum
Little House on the Prarie
Musashi
Beowulf
Greek Myths (not any particular version, I read dozens of versions as a kid and they all run together in my mind.)

Nonfiction
Godel Escher Bach
Zen and the Art of Motorcycle Maintenance (same advice as Moby Dick.)